Investigating the law of tendential fall in the rate of profit based on feedback control

Abstract

The rate of profit is a key element for understanding the movement of capitalism such as technological progress and economic crisis. Even though capitalists seek larger profit rates, there exists a tendency of stagnating or falling profit rates. According to Marx, the rate of profit would tend to decline in the long run as a result of technological progress, termed the law of tendential fall in the profit rate. This article introduces a novel approach based on the discrete-time feedback control mechanism to elucidate Marx's theory. Specifically, this study presents a mechanism and conditions to show how the effort to maximize the profit rate, implemented by designing an “appropriate” control law under the sampling of fiscal years, eventually leads to the gradual decrease in the rate of profit in the long run.